Nothing Special   »   [go: up one dir, main page]

You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (2,101)

Search Parameters:
Keywords = vibration monitoring

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
13 pages, 4562 KiB  
Article
Tool Condition Monitoring Model Based on DAE–SVR
by Xiaoning Sun, Zhifeng Yang, Maojin Xia, Min Xia, Changfu Liu, Yang Zhou and Yuquan Guo
Machines 2025, 13(2), 115; https://doi.org/10.3390/machines13020115 - 1 Feb 2025
Viewed by 256
Abstract
Cutting tools are executive components in metal processing, and tool wear directly affects the quality of the workpiece and processing efficiency; monitoring the change in its state is crucial to avoid accidents and ensure the safety of workers. The traditional monitoring model cannot [...] Read more.
Cutting tools are executive components in metal processing, and tool wear directly affects the quality of the workpiece and processing efficiency; monitoring the change in its state is crucial to avoid accidents and ensure the safety of workers. The traditional monitoring model cannot compress a large amount of cutting data effectively, failing to obtain reliable feature data, and there are some defects in generalization ability and monitoring accuracy. For this purpose, this article takes milling cutters as the research object, and it integrates signals from force sensors, vibration sensors, and acoustic emission sensors, combining the advantages of the denoising autoencoder (DAE) model in data compression and the high monitoring accuracy of the support vector regression (SVR) model, to establish a tool wear monitoring model based on DAE–SVR. The results show that compared with traditional DAE and SVR models in multiple datasets, the maximum improvement in monitoring performance (MAE) is 43.58%. Full article
(This article belongs to the Section Machines Testing and Maintenance)
16 pages, 51859 KiB  
Article
On the Correlation of Cymbals’ Vibrational Behavior and Manufacturing Processes
by Spyros Brezas, Evaggelos Kaselouris, Yannis Orphanos, Makis Bakarezos, Nektarios A. Papadogiannis and Vasilis Dimitriou
Appl. Sci. 2025, 15(3), 1425; https://doi.org/10.3390/app15031425 - 30 Jan 2025
Viewed by 356
Abstract
The complex frequency domain assurance criterion is here applied for the comparison of a pristine to an altered state of a vibrating system. The criterion was originally proposed for the detection of defects in vibrating structures, while in later research studies it has [...] Read more.
The complex frequency domain assurance criterion is here applied for the comparison of a pristine to an altered state of a vibrating system. The criterion was originally proposed for the detection of defects in vibrating structures, while in later research studies it has been successfully used in musical acoustics. In this paper, we evaluate the differences in the vibrational behavior of finished and non-finished cymbals by adopting the proposed correlation criterion. Since idiophones are playable and produce sounds after any manufacturing process, the methodology presented correlates the vibrational state of a cymbal, at any stage of manufacturing, to a reference pristine cymbal. The evaluation of the cymbals is performed by the comparison of finished cymbals with semi-finished and blank 8-inch cymbals of the same material. The correlation criterion is applied to the vibrational measurements of blank, semi-finished, and finished B8 and B20 cymbals. Additionally, commercially available finished cymbals of the same material and geometrical characteristics are introduced in this correlation study. The measuring methodology and the vibration symmetry are discussed, and valuable results and conclusions are presented. The proposed methodology highlights the influence of the manufacturing processes of forming, hammering, and finishing on the vibrational behavior of cymbals, offering manufacturers and drummers a quantifiable criterion for evaluating cymbals’ vibroacoustic performance. Representative evaluations of blanks, semi-finished, and finished cymbals demonstrate the capability of the correlation criterion to monitor, identify, and visualize the vibrational state of any cymbal compared to a pristine reference. This enables the development of a novel methodology for both manufacturers and musicians. Full article
(This article belongs to the Special Issue Vibroacoustic Monitoring: Theory, Methods and Applications)
Show Figures

Figure 1

Figure 1
<p>Measurement setup. Impact hammer (1), accelerometer (2), and measurement grid of 144 points (3) on the B8-1 cymbal.</p>
Full article ">Figure 2
<p>Flowchart of the proposed methodology application for measurements and calculations.</p>
Full article ">Figure 3
<p>SCI values vs. the numbers of measurement points from 14 to 144 by a step of 14, tested for the stability of the calculations, based on the real (solid lines) and on the imaginary (dashed lines) values of CFDACs.</p>
Full article ">Figure 4
<p>CFDACs between FRFs of B8-1 and B8-1, B8-2, B8-3, B8-4, and B8-5 cymbals. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi> Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>Im</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>2</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>Im</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>2</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>3</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>Im</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>3</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math> (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>4</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>Im</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>4</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>5</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>j</b>) <math display="inline"><semantics> <mrow> <mi>Im</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>5</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>SCI calculated by comparing <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>2</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>3</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>4</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>5</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>. Blue: using the real parts of the CFDACs. Red: using the imaginary parts of the CFDACs.</p>
Full article ">Figure 6
<p>The real parts of the CFDACs between the finished B8 cymbal and the blank B8 cymbals. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>2</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>3</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> <mtext> </mtext> </mrow> </semantics></math> (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>4</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>5</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 7
<p>SCI calculated by comparing <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>2</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>3</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>4</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>0</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>8</mn> <mo>‐</mo> <mn>5</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>. Blue: using the real parts of the CFDACs. Red: using the imaginary parts of the CFDACs.</p>
Full article ">Figure 8
<p>The real parts of the CFDACs between semi-finished B20-51 cymbal and the blank and semi-finished cymbals. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>41</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>42</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>43</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>44</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>52</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>53</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>54</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>55</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 9
<p>SCI calculated by comparing <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>41</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>42</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>43</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>44</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>52</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>53</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>54</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>55</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </semantics></math>. Blue: using the real parts of the CFDACs. Red: using the imaginary parts of the CFDACs.</p>
Full article ">Figure 10
<p>Real parts of CFDACs between the finished B20-1 cymbal and the blank and semi-finished B20 cymbals. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>41</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>42</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>43</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>44</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>51</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>f</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>52</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>g</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>53</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> <mo>,</mo> </mrow> </semantics></math> (<b>h</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>54</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>, (<b>i</b>) <math display="inline"><semantics> <mrow> <mi>Re</mi> <mfenced open="{" close="}" separators="|"> <mrow> <msub> <mrow> <mi>CFDAC</mi> </mrow> <mrow> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>1</mn> </mrow> </mrow> </mfenced> </mrow> </msup> <mo>,</mo> <msup> <mrow> <mi>h</mi> </mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mi mathvariant="normal">B</mi> <mn>20</mn> <mo>‐</mo> <mn>55</mn> </mrow> </mrow> </mfenced> </mrow> </msup> </mrow> </msub> </mrow> </mfenced> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Magnitude of the FRFs of the BS20-1 finished cymbal (blue), B20-42 blank cymbal (red, top), and B20-52 semi-finished cymbal (red, bottom) vs. frequency.</p>
Full article ">Figure 12
<p>SCI calculated by using the CFDACs of the finished B20 cymbals and the CFDACs of the blank and semi-finished B20 cymbals.</p>
Full article ">Figure 13
<p>SCI calculated by using the CFDACs of the originally measured FRF matrix and the CFDACs after shifting the rows of the matrix.</p>
Full article ">
15 pages, 4319 KiB  
Article
A Hybrid Deep Transfer Learning Framework for Delamination Identification in Composite Laminates
by Muhammad Haris Yazdani, Muhammad Muzammil Azad, Salman Khalid and Heung Soo Kim
Sensors 2025, 25(3), 826; https://doi.org/10.3390/s25030826 - 30 Jan 2025
Viewed by 351
Abstract
Structural health monitoring (SHM) has proven to be an effective technique to maintain the safety and reliability of laminated composites. Recently, both deep learning and machine learning methodologies have gained popularity in sensor-based SHM. However, machine learning approaches often require tedious manual feature [...] Read more.
Structural health monitoring (SHM) has proven to be an effective technique to maintain the safety and reliability of laminated composites. Recently, both deep learning and machine learning methodologies have gained popularity in sensor-based SHM. However, machine learning approaches often require tedious manual feature extraction, while deep learning models require large training datasets, which may not be feasible. To overcome these limitations, this study presents a hybrid deep transfer learning (HTL) framework to identify delamination in composite laminates. The proposed framework enhances SHM performance by utilizing pre-trained EfficientNet and ResNet models to allow for deep feature extraction with limited data. EfficientNet contributes to this by efficiently scaling the model to capture multi-scale spatial features, while ResNet contributes by extracting hierarchical representations through its residual connections. Vibration signals from piezoelectric (PZT) sensors attached to the composite laminates, consisting of three health states, are used to validate the approach. Compared to the existing transfer learning approaches, the suggested method achieved better performance, hence improving both the accuracy and robustness of delamination detection in composite structures. Full article
(This article belongs to the Special Issue The Intelligent Design of Structure Dynamics and Sensors)
Show Figures

Figure 1

Figure 1
<p>Overview of the hybrid SHM framework for composite laminates.</p>
Full article ">Figure 2
<p>Schematic comparison of (<b>a</b>) normal and (<b>b</b>) residual blocks.</p>
Full article ">Figure 3
<p>A detailed schematic of the ResNet50V2 model and the process of transferring information to the target domain.</p>
Full article ">Figure 4
<p>Architecture of the EfficientNet-based transfer learning model.</p>
Full article ">Figure 5
<p>Experimental setup for data acquisition: (1) LabView PC, (2) excitation DAQ, (3) amplifier for shaker, (4) shaker, (5) composite sample, (6) amplifier for accelerometer, and (7) data acquisition system [<a href="#B32-sensors-25-00826" class="html-bibr">32</a>].</p>
Full article ">Figure 6
<p>Diagram showing the experimental setup used to collect vibrational data from laminated composites.</p>
Full article ">Figure 7
<p>CWT processing of vibrational data into scalograms.</p>
Full article ">Figure 8
<p>The flowchart illustrating the working of all three models.</p>
Full article ">Figure 9
<p>Training curves of transfer learning models (<b>a</b>) EfficientNet, (<b>b</b>) ResNet, and (<b>c</b>) HTL, showing performance over the number of epochs.</p>
Full article ">Figure 10
<p>Illustration of the confusion matrix for (<b>a</b>) EfficientNet, (<b>b</b>) ResNet, and (<b>c</b>) HTL models, using the unseen test datasets.</p>
Full article ">
15 pages, 4205 KiB  
Article
Modal Parameter Identification of the Improved Random Decrement Technique-Stochastic Subspace Identification Method Under Non-Stationary Excitation
by Jinzhi Wu, Jie Hu, Ming Ma, Chengfei Zhang, Zenan Ma, Chunjuan Zhou and Guojun Sun
Appl. Sci. 2025, 15(3), 1398; https://doi.org/10.3390/app15031398 - 29 Jan 2025
Viewed by 367
Abstract
Commonly used methods for identifying modal parameters under environmental excitations assume that the unknown environmental input is a stationary white noise sequence. For large-scale civil structures, actual environmental excitations, such as wind gusts and impact loads, cannot usually meet this condition, and exhibit [...] Read more.
Commonly used methods for identifying modal parameters under environmental excitations assume that the unknown environmental input is a stationary white noise sequence. For large-scale civil structures, actual environmental excitations, such as wind gusts and impact loads, cannot usually meet this condition, and exhibit obvious non-stationary and non-white-noise characteristics. The theoretical basis of the stochastic subspace method is the state-space equation in the time domain, while the state-space equation of the system is only applicable to linear systems. Therefore, under non-smooth excitation, this paper proposes a stochastic subspace method based on RDT. Firstly, this paper uses the random decrement technique of non-stationary excitation to obtain the free attenuation response of the response signal, and then uses the stochastic subspace identification (SSI) method to identify the modal parameters. This not only improves the signal-to-noise ratio of the signal, but also improves the computational efficiency significantly. A non-stationary excitation is applied to the spatial grid structure model, and the RDT-SSI method is used to identify the modal parameters. The identification results show that the proposed method can solve the problem of identifying structural modal parameters under non-stationary excitation. This method is applied to the actual health monitoring of stadium grids, and can also obtain better identification results in frequency, damping ratio, and vibration mode, while also significantly improving computational efficiency. Full article
39 pages, 25363 KiB  
Article
An Agglomerative Clustering Combined with an Unsupervised Feature Selection Approach for Structural Health Monitoring
by Tales Boratto, Heder Soares Bernardino, Alex Borges Vieira, Tiago Silveira Gontijo, Matteo Bodini, Dmitriy A. Martyushev, Camila Martins Saporetti, Alexandre Cury, Flávio Barbosa and Leonardo Goliatt
Infrastructures 2025, 10(2), 32; https://doi.org/10.3390/infrastructures10020032 - 28 Jan 2025
Viewed by 645
Abstract
Structural health monitoring (SHM) is critical for ensuring the safety and longevity of structures, yet existing methodologies often face challenges such as high data dimensionality, lack of interpretability, and reliance on extensive label datasets. Current research in SHM has primarily focused on supervised [...] Read more.
Structural health monitoring (SHM) is critical for ensuring the safety and longevity of structures, yet existing methodologies often face challenges such as high data dimensionality, lack of interpretability, and reliance on extensive label datasets. Current research in SHM has primarily focused on supervised approaches, which require significant manual effort for data labeling and are less adaptable to new environments. Additionally, the large volume of data generated from dynamic structural monitoring campaigns often includes irrelevant or redundant features, further complicating the analysis and reducing computational efficiency. This study addresses these issues by introducing an unsupervised learning approach for SHM, employing an agglomerative clustering model alongside an unsupervised feature selection technique utilizing box-plot statistics. The proposed method is assessed through raw acceleration signals obtained from four dynamic structural monitoring campaigns, including 44 features with temporal, statistical, and spectral information. In addition, these features are also evaluated in terms of their relevance, and the most important ones are selected for a new execution of the computational procedure. The proposed feature selection not only reduces data dimensionality but also enhances model interpretability, improving the clustering performance in terms of homogeneity, completeness, V-measure, and adjusted Rand score. The results obtained for the four analyzed cases provide clear insights into the patterns of behavior and structural anomalies. Full article
21 pages, 28531 KiB  
Article
Vibration-Based Anomaly Detection for Induction Motors Using Machine Learning
by Ihsan Ullah, Nabeel Khan, Sufyan Ali Memon, Wan-Gu Kim, Jawad Saleem and Sajjad Manzoor
Sensors 2025, 25(3), 773; https://doi.org/10.3390/s25030773 - 27 Jan 2025
Viewed by 378
Abstract
Predictive maintenance of induction motors continues to be a significant challenge in ensuring industrial reliability and minimizing downtime. In this study, machine learning techniques are utilized to enhance fault diagnosis through the use of the Machinery Fault Database (MAFAULDA). A detailed extraction of [...] Read more.
Predictive maintenance of induction motors continues to be a significant challenge in ensuring industrial reliability and minimizing downtime. In this study, machine learning techniques are utilized to enhance fault diagnosis through the use of the Machinery Fault Database (MAFAULDA). A detailed extraction of statistical features was performed on multivariate time-series data to capture essential patterns that could indicate potential faults. Three machine learning algorithms—deep neural networks (DNNs), support vector machines (SVMs), and K-nearest neighbors (KNNs)—were applied to the dataset. Optimization strategies were carefully implemented along with oversampling techniques to improve model performance and handle imbalanced data. The results achieved through these models are highly promising. The SVM model demonstrated an accuracy of 95.4%, while KNN achieved an accuracy of 92.8%. Notably, the combination of deep neural networks with fast Fourier transform (FFT)-based autocorrelation features produced the highest performance, reaching an impressive accuracy of 99.7%. These results provide a novel approach to machine learning techniques in enhancing operational health and predictive maintenance of induction motor systems. Full article
(This article belongs to the Special Issue Fault Diagnosis and Vibration Signal Processing in Rotor Systems)
Show Figures

Figure 1

Figure 1
<p>The flowchart of the proposed work: red-dashed box implies the implementation of optimization and oversampling using SVM and KNN; blue-dashed box implies the FFT-based feature extraction applied on DNN.</p>
Full article ">Figure 2
<p>The SpectraQuest machine fault simulator.</p>
Full article ">Figure 3
<p>Receiver operating characteristic (ROC) curves of SVM. (<b>a</b>) Linear SVM ROC. (<b>b</b>) Optimized SVM ROC. (<b>c</b>) Optimized SVM using oversampling ROC.</p>
Full article ">Figure 3 Cont.
<p>Receiver operating characteristic (ROC) curves of SVM. (<b>a</b>) Linear SVM ROC. (<b>b</b>) Optimized SVM ROC. (<b>c</b>) Optimized SVM using oversampling ROC.</p>
Full article ">Figure 4
<p>Receiver operating characteristic (ROC) curves of KNN. (<b>a</b>) Unoptimized KNN ROC, (<b>b</b>) Optimized KNN ROC, (<b>c</b>) Oversampled Optimized KNN ROC.</p>
Full article ">Figure 5
<p>Deep neural network architecture.</p>
Full article ">Figure 6
<p>Analysis of 11 features in normal rotational sequences (737 rpm to 3686 rpm).</p>
Full article ">Figure 7
<p>Feature analysis under 6 g imbalance: consistently maintained rotations.</p>
Full article ">Figure 8
<p>Feature analysis under the 10 g imbalance: stable rotational characteristics.</p>
Full article ">Figure 9
<p>Feature analysis under the 15 g imbalance: assessing rotational stability.</p>
Full article ">Figure 10
<p>Feature analysis under the 20 g imbalance: dynamical variations.</p>
Full article ">Figure 11
<p>Feature analysis under the 25 g imbalance: investigating system resilience.</p>
Full article ">Figure 12
<p>Feature analysis under a 30 g imbalance: limitations on rotational frequencies.</p>
Full article ">Figure 13
<p>Feature analysis under a 35 g imbalance.</p>
Full article ">Figure 14
<p>Faulty and normal classification using SVM.</p>
Full article ">Figure 14 Cont.
<p>Faulty and normal classification using SVM.</p>
Full article ">Figure 15
<p>Faulty and normal classification using KNN.</p>
Full article ">Figure 15 Cont.
<p>Faulty and normal classification using KNN.</p>
Full article ">Figure 16
<p>Faulty and normal classification using DNN.</p>
Full article ">
29 pages, 11104 KiB  
Article
Structural Health Assessment of a Reinforced Concrete Building in Valparaíso Under Seismic and Environmental Shaking: A Foundation for IoT-Driven Digital Twin Systems
by Sebastián Lozano-Allimant, Alvaro Lopez, Miguel Gomez, Edison Atencio, José Antonio Lozano-Galant and Sebastian Fingerhuth
Appl. Sci. 2025, 15(3), 1202; https://doi.org/10.3390/app15031202 - 24 Jan 2025
Viewed by 434
Abstract
Structural health monitoring is vital for the safety and longevity of infrastructure, particularly in seismic zones. This study focuses on identifying the dynamic properties of a reinforced concrete building in Chile’s Valparaíso region. Using an experimental approach, the study compares ambient vibration records, [...] Read more.
Structural health monitoring is vital for the safety and longevity of infrastructure, particularly in seismic zones. This study focuses on identifying the dynamic properties of a reinforced concrete building in Chile’s Valparaíso region. Using an experimental approach, the study compares ambient vibration records, seismic events (moment magnitude > 4), and data collected during adjacent construction activities. Force-balanced accelerometers were used for vibration measurements. The analysis employs the Stochastic Subspace Identification with Covariances (SSI-COV) method within an operational modal analysis framework to extract the building’s modal parameters without requiring artificial excitations. This technique effectively identifies modal characteristics under different vibration sources, making it suitable for evaluating the structural condition under diverse loading conditions. The findings reveal the building’s modes and frequencies, offering critical insights for maintenance and management of infrastructure. Little to no variations were observed in the identified frequencies of the building when working with different types of input data. These data support the integration of real-time IoT systems for continuous monitoring, providing a foundation for future digital twin applications. These advancements facilitate early deterioration detection, enhancing resilience in seismic environments. Full article
Show Figures

Figure 1

Figure 1
<p>Methodological scheme of the SSI-COV application for structural health monitoring.</p>
Full article ">Figure 2
<p>Building representation: (<b>a</b>) photograph of the building and (<b>b</b>) digital model. Courtesy of the School of Civil Engineering, PUCV.</p>
Full article ">Figure 3
<p>Sensor distribution in the building: (<b>a</b>) upper floors (3rd to 6th levels), and (<b>b</b>) basement.</p>
Full article ">Figure 4
<p>SL06 ACEBOX triaxial accelerometer installed in the building.</p>
Full article ">Figure 5
<p>Exemplary acceleration records: (<b>a</b>) ambient vibration, (<b>b</b>) a seismic event, and (<b>c</b>) adjacent construction.</p>
Full article ">Figure 6
<p>Dates with synchronized data available for different sensor configurations.</p>
Full article ">Figure 7
<p>Stable frequencies in the X direction per order with 400 Hz sampling for 2022–2023 ambient vibration. (<b>a</b>) Tolerances: <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ζ</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.04, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>M</mi> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01. (<b>b</b>) Tolerances: <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ζ</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> =<math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mrow> <mi>M</mi> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01.</p>
Full article ">Figure 8
<p>Stable frequencies per order in the X and Y directions (downsampling to 30 Hz, &gt;10% participation) for 2022–2023 ambient vibration. (<b>a</b>) X direction: <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ζ</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> =<math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mrow> <mi>M</mi> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01. (<b>b</b>) Y direction: <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>f</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ζ</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = <math display="inline"><semantics> <mrow> <mo> </mo> <msub> <mrow> <mi>M</mi> <mi>A</mi> <mi>C</mi> </mrow> <mrow> <mi>t</mi> <mi>o</mi> <mi>l</mi> </mrow> </msub> </mrow> </semantics></math> = 0.01.</p>
Full article ">Figure 9
<p>Identified frequencies in the X direction per order for data filtered at 2.5 Hz for 2022–2023 ambient vibration (only frequencies with &gt;10% participation).</p>
Full article ">Figure 10
<p>Frequency grouping and boundaries across model orders using k-means clustering.</p>
Full article ">Figure 11
<p>Boxplots of orders grouped by a frequency threshold of 2.5 Hz for 2022–2023 ambient vibration. (<b>a</b>) Orders with frequencies greater than 2.5 Hz. (<b>b</b>) Orders with frequencies less than 2.5 Hz.</p>
Full article ">Figure 12
<p>Identified frequencies in the X direction per order for data filtered at 2.5 Hz for 2024 ambient vibration (only frequencies with &gt;10% participation are shown).</p>
Full article ">Figure 13
<p>Frequency grouping and boundaries across model orders using k-means clustering.</p>
Full article ">Figure 14
<p>Boxplots of orders grouped by a frequency threshold of 2.5 Hz for 2024 ambient vibration. (<b>a</b>) Orders with frequencies greater than 2.5 Hz. (<b>b</b>) Orders with frequencies less than 2.5 Hz.</p>
Full article ">Figure 15
<p>Identified frequencies in the X direction per order for data filtered at 2.5 Hz for seismic events (only frequencies with &gt;10% participation are shown).</p>
Full article ">Figure 16
<p>Boxplots of orders grouped by a frequency threshold of 2.5 Hz for seismic events. (<b>a</b>) Orders with frequencies greater than 2.5 Hz. (<b>b</b>) Orders with frequencies less than 2.5 Hz.</p>
Full article ">Figure 17
<p>Identified frequencies in the X direction per order for data filtered at 2.5 Hz for adjacent construction vibrations (only frequencies with &gt;10% participation are shown).</p>
Full article ">Figure 18
<p>Boxplots of orders grouped by a frequency threshold of 2.5 Hz for adjacent construction vibrations. (<b>a</b>) Orders with frequencies greater than 2.5 Hz. (<b>b</b>) Orders with frequencies less than 2.5 Hz.</p>
Full article ">Figure 19
<p>Temporal evolution of the frequencies for system order 24.</p>
Full article ">
19 pages, 3105 KiB  
Article
Investigating the Effect of Vibration Signal Length on Bearing Fault Classification Using Wavelet Scattering Transform
by Suparerk Janjarasjitt
Sensors 2025, 25(3), 699; https://doi.org/10.3390/s25030699 - 24 Jan 2025
Viewed by 373
Abstract
Bearing condition monitoring and prognosis are crucial tasks for ensuring the proper operation of rotating machinery and mechanical systems. Vibration signal analysis is one of the most effective techniques for bearing condition monitoring and prognosis. In this study, the wavelet scattering transform, derived [...] Read more.
Bearing condition monitoring and prognosis are crucial tasks for ensuring the proper operation of rotating machinery and mechanical systems. Vibration signal analysis is one of the most effective techniques for bearing condition monitoring and prognosis. In this study, the wavelet scattering transform, derived from wavelet transforms and incorporating concepts from scattering transform and convolutional network architectures, was utilized to extract quantitative features from vibration signals. The number of wavelet scattering coefficients obtained from vibration signals of different lengths varied due to the use of predefined wavelet and scaling filters in the wavelet scattering network. Additionally, these wavelet scattering coefficients are associated with different scattering paths within the corresponding wavelet scattering networks. Eight different lengths of vibration signals, associated with fifteen classes of rolling element bearing faults and conditions, were investigated using wavelet scattering feature extraction. The classes of rolling element bearing faults and conditions included normal bearings as well as ball and inner race faults with various fault diameters ranging from 0.007 inches to 0.028 inches. For the specific dataset validated, the computational results indicated that excellent bearing fault classification was achievable using wavelet scattering feature vectors derived from vibration signals with lengths of at least 6000 samples. Full article
Show Figures

Figure 1

Figure 1
<p>Exemplary vibration signal epochs, each with a length of 600 samples, associated with each class.</p>
Full article ">Figure 2
<p>Exemplary vibration signal epochs, each with a length of 6000 samples, associated with each class.</p>
Full article ">Figure 3
<p>Exemplary vibration signal epochs, each with a length of 15,000 samples, associated with each class.</p>
Full article ">Figure 4
<p>Comparison of top two wavelet scattering features of vibration signal epochs for each length.</p>
Full article ">Figure 5
<p>Learning curve of the bearing fault classifications for each epoch length.</p>
Full article ">Figure 6
<p>The range of overall accuracy of the bearing fault classifications for each epoch length.</p>
Full article ">
20 pages, 1246 KiB  
Review
Roping Prediction Versus Detection: Could Prediction Be Possible?
by Lin Yang, Lei Chen, Difan Tang, Massimiliano Zanin, Chris Aldrich and Richmond Asamoah
Minerals 2025, 15(2), 110; https://doi.org/10.3390/min15020110 - 23 Jan 2025
Viewed by 349
Abstract
Roping is a hydrocyclone failure mode that reduces separation efficiency, negatively impacting both the comminution circuit and downstream flotation processes. Therefore, detection of roping as early as possible is crucial in maintaining the normal performance of physical separation and linked processes. Most importantly, [...] Read more.
Roping is a hydrocyclone failure mode that reduces separation efficiency, negatively impacting both the comminution circuit and downstream flotation processes. Therefore, detection of roping as early as possible is crucial in maintaining the normal performance of physical separation and linked processes. Most importantly, instead of detecting roping after it happens, could roping be predicted even before it arises? This review examines various detection methods, including mechanical, tomography, vibration, acoustic, and image processing, highlighting their cost and ability to monitor parameters like air core size, spray angle, and solid concentration. While most current methods detect roping only after it happens, predictive approaches could save time and costs. A promising solution combines pressure and vibration sensing with advanced signal processing, showing early potential to transform roping prediction and improve operational efficiency. This review highlights research gaps across various methods, underscores the importance of developing predictive capabilities for hydrocyclone operations, and outlines the essential conditions and future priorities for achieving roping prediction. Full article
Show Figures

Figure 1

Figure 1
<p>The structure of a hydrocyclone.</p>
Full article ">Figure 2
<p>The schematic of the roping detection equipment innovated by Hulbert [<a href="#B10-minerals-15-00110" class="html-bibr">10</a>].</p>
Full article ">Figure 3
<p>The schematic of the roping detection equipment innovated by Rakesh et al. [<a href="#B23-minerals-15-00110" class="html-bibr">23</a>].</p>
Full article ">Figure 4
<p>Schematic of experimental setup (redrawn from Nayak et al. [<a href="#B37-minerals-15-00110" class="html-bibr">37</a>]).</p>
Full article ">Figure 5
<p>Schematic of a 125 mm hydrocyclone test rig (redrawn from Hou et al. [<a href="#B55-minerals-15-00110" class="html-bibr">55</a>]).</p>
Full article ">Figure 6
<p>Principle of the laser–optical measuring device (redrawn from Neesse et al. [<a href="#B9-minerals-15-00110" class="html-bibr">9</a>]).</p>
Full article ">Figure 7
<p>The schematic of the underflow width measurement (modified from Janse van Vuuren et al. [<a href="#B83-minerals-15-00110" class="html-bibr">83</a>]).</p>
Full article ">Figure 8
<p>Air core in hydrocyclone (redrawn from Li et al. [<a href="#B88-minerals-15-00110" class="html-bibr">88</a>]). The blue line represents the path of water flow.</p>
Full article ">
27 pages, 18817 KiB  
Article
Research on Bolt Loosening Mechanism Under Sine-on-Random Coupling Vibration Excitation
by Jiangong Du, Yuanying Qiu and Jing Li
Machines 2025, 13(2), 80; https://doi.org/10.3390/machines13020080 - 23 Jan 2025
Viewed by 393
Abstract
This paper primarily investigates the mechanism of bolt loosening under the Sine-on-Random (SOR) vibration excitation. Firstly, a theoretical model of bolt loosening response under the SOR synthesized excitation is established by a time–frequency conversion method, which converts the sine excitation into Power Spectrum [...] Read more.
This paper primarily investigates the mechanism of bolt loosening under the Sine-on-Random (SOR) vibration excitation. Firstly, a theoretical model of bolt loosening response under the SOR synthesized excitation is established by a time–frequency conversion method, which converts the sine excitation into Power Spectrum Density (PSD) expression in the frequency domain and superimposes it with random vibration excitation to obtain the SOR synthesized excitation spectrum. Then, by means of a four-bolt fastened structure, the bolt loosening mechanisms under both the sine and random vibration excitation are deeply studied, respectively. Ultimately, based on the time–frequency conversion method of SOR synthesized excitation, the bolt loosening responses of the structure under SOR excitation with different tightening torques are analyzed. Furthermore, a three-stage criterion including the Steady Stage, Transition Stage, and Loosen Stage for bolt loosening under SOR excitation is revealed, and the relationship among the SOR synthesized vibration responses and the two forms of single vibration responses is explored based on a corrective energy superposition method by introducing the weight factors of the two single vibration responses under different tightening torques. Finally, test verifications for the four-bolt fastened structure are conducted and good consistencies with the results of the Finite Element Analysis (FEA) are shown. This study provides valuable insights into the detection and prevention of loosening in bolted connection structures under multi-source vibration environments and has important engineering reference significance. Full article
Show Figures

Figure 1

Figure 1
<p>Model of the 4-bolt fastened structure.</p>
Full article ">Figure 2
<p>Schematic diagram of the 4-bolt fastened structure.</p>
Full article ">Figure 3
<p>Normal strain responses of the monitored points within 0.1 s under 15 N·m tightening torque.</p>
Full article ">Figure 4
<p>Strain RMS of FEA results varying with tightening torque under sine vibration.</p>
Full article ">Figure 5
<p>Random vibration excitation spectrum.</p>
Full article ">Figure 6
<p>FEA strain RMS varying with tightening torques under random vibration.</p>
Full article ">Figure 7
<p>Diagram of SOR synthesized excitation in different domains.</p>
Full article ">Figure 8
<p>Strain response PSD of the monitored points under SOR excitation with 15 N·m tightening torque.</p>
Full article ">Figure 9
<p>Curves of strain RMS of monitored points versus tightening torques under SOR synthesized excitation.</p>
Full article ">Figure 10
<p>Comparison curves of strain RMS at monitored points under three forms of vibration.</p>
Full article ">Figure 11
<p>The calculation flowsheet for all optimal weight factors <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>Curves of weight factors <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>b</mi> <mrow> <msub> <mi>T</mi> <mi>i</mi> </msub> </mrow> </msub> </mrow> </semantics></math> as a function of tightening torque.</p>
Full article ">Figure 13
<p>The test devices and test specimen.</p>
Full article ">Figure 14
<p>The test structure and distribution of the strain gauges.</p>
Full article ">Figure 15
<p>The torque wrench.</p>
Full article ">Figure 16
<p>Strain sampling data under sine vibration excitation with 15 N·m tightening torque.</p>
Full article ">Figure 17
<p>RMS results of strain response at the six monitored points under sine vibration test.</p>
Full article ">Figure 18
<p>Comparison between the test and FEA results of strain RMS at monitored points under sine vibration.</p>
Full article ">Figure 19
<p>Strain sampling data under random vibration excitation with 15 N·m tightening torque.</p>
Full article ">Figure 20
<p>RMS results of strain response at the six monitored points under random vibration test.</p>
Full article ">Figure 21
<p>Comparison between the test and FEA results of strain RMS at monitored points under random vibration.</p>
Full article ">
16 pages, 3634 KiB  
Article
A Reservoir Dam Monitoring Technology Integrating Improved ABC Algorithm and SVM Algorithm
by Yunqian Xu, Tengfei Bao, Mingdao Yuan and Shu Zhang
Water 2025, 17(3), 302; https://doi.org/10.3390/w17030302 - 22 Jan 2025
Viewed by 402
Abstract
A reservoir dam is a water conservancy project with large investment and high social and economic benefits, which plays an irreplaceable role in flood control, power generation, water storage, and urban water supply. There is a risk of accidents in the process of [...] Read more.
A reservoir dam is a water conservancy project with large investment and high social and economic benefits, which plays an irreplaceable role in flood control, power generation, water storage, and urban water supply. There is a risk of accidents in the process of reservoir dams, so dam monitoring is an important means to achieve the safe operation of reservoirs. In this paper, taking advantage of the high-dimensional and nonlinear characteristics of dam monitoring data samples, the fusion-improved ABC (artificial bee colony) algorithm is introduced, and the SVM (support vector machine) algorithm is used to optimize the penalty factor and kernel function parameters. The test results of the ABC and SVM algorithm are relatively stable, with small fluctuation amplitude, which can continuously monitor water level, pore water pressure, dam deformation, temperature, humidity, vibration, and other indicators is less than 10%, which is significantly lower than the standard ABC algorithm, the standard ANN algorithm, and the standard SVM algorithm. The independence and characteristics of the ABC–SVM algorithm are significantly higher, and the correlation is 0.03, the RMS (root mean square) is 0.2334, which is lower than that of the standard ABC algorithm of 0.09, and the standard ANN algorithm of 0.8. The stability of the results and performance stability are analyzed, which is greater than 90%. The ABC and SVM is used to predict the displacement and deformation law of the reservoir dam. Full article
Show Figures

Figure 1

Figure 1
<p>Research flow chart.</p>
Full article ">Figure 2
<p>Drone Aerial View of the Dam. (<b>a</b>) Drone aerial view from the downstream perspective. (<b>b</b>) Drone aerial view from the upstream perspective.</p>
Full article ">Figure 3
<p>Part view of the safety monitoring point distribution map.</p>
Full article ">Figure 4
<p>Plausibility of dam detection data.</p>
Full article ">Figure 5
<p>Comparison of test results from different algorithms.</p>
Full article ">Figure 6
<p>Comprehensive comparison of dam monitoring accuracy.</p>
Full article ">Figure 7
<p>Predictability of different algorithms versus actual results.</p>
Full article ">Figure 8
<p>Phase diagram of dam analysis results.</p>
Full article ">Figure 9
<p>Scatter plot analysis of dam data monitoring results.</p>
Full article ">
20 pages, 1816 KiB  
Article
Accurate Cardiac Duration Detection for Remote Blood Pressure Estimation Using mm-Wave Doppler Radar
by Shengze Wang, Mondher Bouazizi, Siyuan Yang and Tomoaki Ohtsuki
Sensors 2025, 25(3), 619; https://doi.org/10.3390/s25030619 - 21 Jan 2025
Viewed by 567
Abstract
This study introduces a radar-based model for estimating blood pressure (BP) in a touch-free manner. The model accurately detects cardiac activity, allowing for contactless and continuous BP monitoring. Cardiac motions are considered crucial components for estimating blood pressure. Unfortunately, because these movements are [...] Read more.
This study introduces a radar-based model for estimating blood pressure (BP) in a touch-free manner. The model accurately detects cardiac activity, allowing for contactless and continuous BP monitoring. Cardiac motions are considered crucial components for estimating blood pressure. Unfortunately, because these movements are extremely subtle and can be readily obscured by breathing and background noise, accurately detecting these motions with a radar system remains challenging. Our approach to radar-based blood pressure monitoring in this research primarily focuses on cardiac feature extraction. Initially, an integrated-spectrum waveform is implemented. The method is derived from the short-time Fourier transform (STFT) and has the ability to capture and maintain minute cardiac activities. The integrated spectrum concentrates on energy changes brought about by short and high-frequency vibrations, in contrast to the pulse-wave signals used in previous works. Hence, the interference caused by respiration, random noise, and heart contractile activity can be effectively eliminated. Additionally, we present two approaches for estimating cardiac characteristics. These methods involve the application of a hidden semi-Markov model (HSMM) and a U-net model to extract features from the integrated spectrum. In our approach, the accuracy of extracted cardiac features is highlighted by the notable decreases in the root mean square error (RMSE) for the estimated interbeat intervals (IBIs), systolic time, and diastolic time, which were reduced by 87.5%, 88.7%, and 73.1%. We reached a comparable prediction accuracy even while our subject was breathing normally, despite previous studies requiring the subject to hold their breath. The diastolic BP (DBP) error of our model is 3.98±5.81 mmHg (mean absolute difference ± standard deviation), and the systolic BP (SBP) error is 6.52±7.51 mmHg. Full article
(This article belongs to the Special Issue Analyzation of Sensor Data with the Aid of Deep Learning)
Show Figures

Figure 1

Figure 1
<p>An illustration of (<b>a</b>) conventional assumption on systolic and diastolic timing extraction and (<b>b</b>) actual systolic and diastolic timings from ECG waveform.</p>
Full article ">Figure 2
<p>The system model and the setup of the Doppler sensor for capturing the heartbeat signal.</p>
Full article ">Figure 3
<p>An illustration of the heart parts.</p>
Full article ">Figure 4
<p>Flowchart of the proposed method.</p>
Full article ">Figure 5
<p>(<b>a</b>) The spectrogram of the conventional pulse wave signal; (<b>b</b>) the spectrogram of the higher-frequency radar signal selected in our work.</p>
Full article ">Figure 6
<p>Integrated spectrum and pulse wave with ECG as gold standard.</p>
Full article ">Figure 7
<p>Example of an HSMM algorithm.</p>
Full article ">Figure 8
<p>The estimated state change generated by HSMM.</p>
Full article ">Figure 9
<p>Example of a U-net structure.</p>
Full article ">Figure 10
<p>An illustration of (<b>A</b>) shows the label are generated from the ECG signal. (<b>B</b>) shows the comparison between Integrated spectrum and the generated label.</p>
Full article ">Figure 11
<p>The integrated spectrum, state changes, and U-net results compared with the R-peaks and end of the T-wave in the ECG.</p>
Full article ">
18 pages, 7358 KiB  
Article
Multi-Point Optical Flow Cable Force Measurement Method Based on Euler Motion Magnification
by Jinzhi Wu, Bingyi Yan, Yu Xue, Jie Qin, Deqing You and Guojun Sun
Buildings 2025, 15(3), 311; https://doi.org/10.3390/buildings15030311 - 21 Jan 2025
Viewed by 412
Abstract
This study introduces a multi-point optical flow cable force measurement method based on Euler motion amplification to address challenges in accurately measuring cable displacement under small displacement conditions and mitigating background interference in complex environments. The proposed method combines phase-based magnification with an [...] Read more.
This study introduces a multi-point optical flow cable force measurement method based on Euler motion amplification to address challenges in accurately measuring cable displacement under small displacement conditions and mitigating background interference in complex environments. The proposed method combines phase-based magnification with an optical flow method to enhance small displacement features and improve SNR (signal-to-noise ratio) in cable displacement tracking. By leveraging magnified motion data and integrating auxiliary feature points, the approach compensates for equipment-induced vibrations and background noise, allowing for precise cable displacement measurement and the identification of vibration modes. The methodology was validated using a scaled model of a cable net structure. The results demonstrate the method’s effectiveness, achieving a significantly higher SNR (e.g., from 7.5 dB to 22.24 dB) compared to traditional optical flow techniques. Vibration frequency errors were reduced from 6.2% to 1.5%, and cable force errors decreased from 11.38% to 3.13%. The multi-point optical flow cable force measurement method based on Euler motion magnification provides a practical and reliable solution for non-contact cable force measurement, offering potential applications in structural health monitoring and the maintenance of bridges and high-altitude structures. Full article
Show Figures

Figure 1

Figure 1
<p>Flowchart of multi−point optical flow cable force measurement method based on Euler motion magnification.</p>
Full article ">Figure 2
<p>Schematic diagram of the scale model.</p>
Full article ">Figure 3
<p>Structural component diagram.</p>
Full article ">Figure 4
<p>Schematic diagram of the inclined cable position.</p>
Full article ">Figure 5
<p>Schematic diagram of the acceleration sensor position.</p>
Full article ">Figure 6
<p>Selection of feature points of the traditional optical flow method.</p>
Full article ">Figure 7
<p>Characteristic point selection of the multi-point optical flow method.</p>
Full article ">Figure 8
<p>Comparison of SNR at different magnifications.</p>
Full article ">Figure 9
<p>Comparison of the oblique cable displacement response curve. (<b>a</b>) XS-1-P<sub>1</sub> comparison of the node time shift curve; (<b>b</b>) XS-2-P<sub>1</sub> comparison of the node time shift curve; (<b>c</b>) XS-3-P<sub>1</sub> comparison of the node time shift curve; (<b>d</b>) XS-4-P<sub>1</sub> comparison of the node time shift curve.</p>
Full article ">Figure 10
<p>The cable spectrum data are collected by high-speed camera. (<b>a</b>) Comparison of the Spectrum Diagram for Node XS1-P<sub>1</sub>; (<b>b</b>) comparison of the Spectrum Diagram for Node XS2-P<sub>1</sub>; (<b>c</b>) comparison of the Spectrum Diagram for Node XS3-P<sub>1</sub>; (<b>d</b>) comparison of the Spectrum Diagram for Node XS4-P<sub>1</sub>.</p>
Full article ">Figure 11
<p>Frequency error comparison diagram.</p>
Full article ">Figure 12
<p>Cable vibration mode shape. (<b>a</b>) XS-1 vibration mode shape; (<b>b</b>) XS-2 vibration mode shape; (<b>c</b>) XS-3 vibration mode shape; (<b>d</b>) XS-4 vibration mode shape.</p>
Full article ">Figure 13
<p>Cable force comparison diagram.</p>
Full article ">Figure 14
<p>Cable force error comparison diagram.</p>
Full article ">
29 pages, 9686 KiB  
Article
A Fault Early Warning Method Based on Auto-Associative Kernel Regression and Auxiliary Classifier Generative Adversarial Network (AAKR-ACGAN) of Gas Turbine Compressor Blades
by Yimin Zhu, Xiaoyi Zhang and Mingyu Luo
Energies 2025, 18(3), 461; https://doi.org/10.3390/en18030461 - 21 Jan 2025
Viewed by 315
Abstract
The compressor blades of the gas turbine continually operate under extreme conditions, including elevated temperature, increased pressure, rapid rotation speed, and high-load environments, and are also subjected to complex vibrations, which inevitably lead to performance degradation and failures. Early fault warning based on [...] Read more.
The compressor blades of the gas turbine continually operate under extreme conditions, including elevated temperature, increased pressure, rapid rotation speed, and high-load environments, and are also subjected to complex vibrations, which inevitably lead to performance degradation and failures. Early fault warning based on historical operation data and real-time working conditions can enhance the safety and economy of gas turbines, preventing severe accidents. However, previous studies often faced challenges, such as a lack of fault data, imbalanced datasets, and low data utilization, which limited the accuracy of the algorithms. This study proposes a fault warning technique for gas turbine compressor blades based on AAKR-ACGAN. First, a digital twin model of the gas turbine is constructed using long-term operation data and simulation data from the mechanism model. Then, an auto-associative kernel regression (AAKR) model is used for the fault warning, monitoring multiple parameters to provide effective early warnings of potential faults. Additionally, an auxiliary classifier generative adversarial network (ACGAN) is employed to fully extract hidden data features of the fault points, balance the dataset, and accurately simulate the process of fault occurrence and development. The proposed approach is utilized for the early detection of faults in the compressor blades of a high-capacity gas turbine, and its precision and applicability are confirmed. The multisource early warning indicator can provide an early warning of a failure up to one year in advance of its occurrence. It was also able to detect a severe surge that occurred six months before the failure, which is speculated to be one of the causes that led to the failure. Full article
(This article belongs to the Section I2: Energy and Combustion Science)
Show Figures

Figure 1

Figure 1
<p>Gas turbine whole-system mechanistic model.</p>
Full article ">Figure 2
<p>Compressor mechanistic model.</p>
Full article ">Figure 3
<p>Wavelet denoising process.</p>
Full article ">Figure 4
<p>K-means clustering algorithm flowchart.</p>
Full article ">Figure 5
<p>Data dimensionality reduction flowchart.</p>
Full article ">Figure 6
<p>AAKR calculation flowchart.</p>
Full article ">Figure 7
<p>Multivariable multiscale permutation entropy calculation flowchart.</p>
Full article ">Figure 8
<p>Basic structure of ACGAN model.</p>
Full article ">Figure 9
<p>Simulation data of mechanism model (normal operation of gas turbine).</p>
Full article ">Figure 10
<p>Simulation data of mechanism model (with fault injection).</p>
Full article ">Figure 11
<p>Photograph of gas turbine field fault.</p>
Full article ">Figure 12
<p>Comparison of curves before and after wavelet denoising.</p>
Full article ">Figure 13
<p>Variance explained by principal components.</p>
Full article ">Figure 14
<p>Bar chart of contribution of each dimension to principal components.</p>
Full article ">Figure 15
<p>Prediction results of each principal component based on AAKR mode.</p>
Full article ">Figure 16
<p>Fault data image (after normalization).</p>
Full article ">Figure 17
<p>Fault data image (after 2D wavelet transform).</p>
Full article ">Figure 18
<p>Generator loss curve and performance evaluation.</p>
Full article ">Figure 19
<p>Fault data sample.</p>
Full article ">Figure 19 Cont.
<p>Fault data sample.</p>
Full article ">Figure 20
<p>Mean squared error alert results.</p>
Full article ">Figure 21
<p>Bayesian confidence alert results.</p>
Full article ">Figure 22
<p>Multivariate multiscale permutation entropy calculation results.</p>
Full article ">Figure 23
<p>CUSUM alert results.</p>
Full article ">
24 pages, 3552 KiB  
Review
State-of-the-Art Detection and Diagnosis Methods for Rolling Bearing Defects: A Comprehensive Review
by Bojun Sun, Zixin Sheng, Peng Song, Huilin Sun, Fei Wang, Xiaogang Sun and Junyan Liu
Appl. Sci. 2025, 15(2), 1001; https://doi.org/10.3390/app15021001 - 20 Jan 2025
Viewed by 700
Abstract
Rolling bearings are essential transmission and support components in aircraft engines, playing a critical role in ensuring their safe and stable operation. Rolling bearing faults have a significant impact and should not be ignored. The effective diagnosis of bearing faults has always been [...] Read more.
Rolling bearings are essential transmission and support components in aircraft engines, playing a critical role in ensuring their safe and stable operation. Rolling bearing faults have a significant impact and should not be ignored. The effective diagnosis of bearing faults has always been a critical requirement for ensuring reliable operation. With the increasing demands of modern manufacturing to reduce costs and improve quality, the development of advanced bearing fault detection methods has become indispensable. This paper presents the brief review of recent trends in research on bearing failure modes, bearing fault detection and diagnosis methods, and development trends and prospects. This article provides a comprehensive review of the existing fault diagnosis methods for rolling bearings in four aspects: the integration of advanced sensor technology and advanced data processing technology, multimodal fusion, intelligent detection, and real-time monitoring. It discusses methods based on vibration analysis, acoustic methods, current-based methods, electromagnetic methods, infrared methods, radiographic methods, visual methods, and intelligent detection methods. This study reveals that the application of intelligent detection technology, multimodal fusion detection technology, and real-time online monitoring technology has achieved favorable results. In the future, bearing fault detection will develop in a more intelligent, integrated, and real-time direction. Full article
Show Figures

Figure 1

Figure 1
<p>Rolling bearing structure. (<b>a</b>) Deep groove ball bearing. (<b>b</b>) Cylindrical roller bearing. 1—inner ring; 2—outer ring; 3—rolling elements; 4—cage.</p>
Full article ">Figure 2
<p>Bearing failure modes.</p>
Full article ">Figure 3
<p>Principle of vibration analysis: The vibration analysis process generally includes steps such as data acquisition, signal preprocessing, feature extraction, and fault diagnosis. First, the bearing’s vibration signals are collected using sensors, followed by filtering and denoising to improve analysis accuracy. Then, key features are extracted using time domain, frequency domain, and time–frequency analysis methods to determine whether faults exist and identify their types.</p>
Full article ">Figure 4
<p>Principle of acoustic signal detection: The detection process generally consists of high-frequency signal acquisition, signal preprocessing, feature extraction, and fault diagnosis. First, high-frequency signals generated during operation are collected using acoustic sensors. After amplifying the signals, specific high-frequency components are extracted, and the acoustic signals are processed to extract feature parameters. These feature signals are typically used to identify specific fault patterns.</p>
Full article ">Figure 5
<p>Principle of current signal detection: The detection process generally consists of current signal acquisition, signal preprocessing, feature extraction, and fault diagnosis.</p>
Full article ">Figure 6
<p>Principle of electromagnetic detection.</p>
Full article ">Figure 7
<p>Principle of infrared thermography.</p>
Full article ">Figure 8
<p>Principle of radiographic detection: When the radiation passes through the object being inspected, the absorption capacity of defective and non-defective parts is different.</p>
Full article ">Figure 9
<p>Principle of vision detection: Uses high-definition cameras or industrial cameras to capture images of bearing surfaces, and then identify cracks, wear, scratches, contaminants, or other surface defects through image processing and algorithm analysis.</p>
Full article ">Figure 10
<p>Principle of intelligent detection.</p>
Full article ">Figure 11
<p>Development trends and prospects.</p>
Full article ">
Back to TopTop